Mahowaldean elements, symplectic bordism and framed hypersurfaces

Mahowaldean elements, symplectic bordism and framed hypersurfaces

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Andrew Baker, University of Glasgow

Zoom link: https://princeton.zoom.us/j/96282936122

 

In the 1970s Mark Mahowald constructed an infinite family of stable homotopy elements systematically detected in the 2-line of the Adams spectral sequence. I will review the construction then give a modified version which has some good features:

1) These elements map to 0 in the symplectic bordism ring.

2) They are detected by primary operations in symplectic bordism and so are detected in the 1-line of the symplectic bordism Adams-Novikov spectral sequence.

Actually the same can be shown to apply to Mahowald's original elements but this requires slightly different methods. 

I will also explain how to construct framed hypersurfaces which represent Mahowald's elements in framed bordism; this uses unstable properties of dual Brown-Gitler spaces proved in the 1990s.